Theory of pair production and radiation in inhomogeneous strong electromagnetic fields

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In this project, we have studied radiation from relativistic electrons/pasitmns and pair production by gamma-rays in inhomogeneous strong electromagnetic fields and other problems related with the vacuum stability under the critical field.First, we have developed a theory of free-bound pair production by relativistic ions. It should be noted that when a relativistic ion enters a crystal along the major axis, the ion feels the crystal field that is equivalent to the periodic pulse of coherent photons which may be regarded as "virtual X-ray laser". At the rest frame of the ion the field strength may become beyond the critical field. In that case it is possible for the ion to produce an electron in its bound state: the bound-state pair production. This process is not only important for the investigating the strong-field QED theory but also for the application to producing antihydrogens or exotic atoms. We have calculated this process by using the plane wave for the final state of produced positron and the relativistic hydrogen like state for the final state of produced electron. By comparing our result with that of Muller, et al., which assume the use of a future X-ray laser, we have found that a crystal with realistic thickness gives larger pair production probability than that of Muller, et al..Second, we have considered the induced type of pair production by using a wave packet under the condition that a relativistic electron enters the crystal axial electric field (10^<12>V/cm). This situation is equivalent to the Mein paradox if we see it in the electron rest frame. We have numerically calculated the motion of the wave packet for the purpose of investigating the Klein paradox type pair production Also, as a fundamental investigation, we have calculated the motion of the wave packet by using Nelson's stochastic mechanics.